The achievement of optimal lifetime and efficiency in stationary battery energy storage systems (BESS) is crucial and may require custom-made operational strategies for each grid application. This work focuses on addressing one of the key operational challenges: power distribution among the sub-units of a BESS, which leads to uneven aging and affects the overall usable capacity of a multi-pack battery system. While adjusting power setpoints of these sub-units can improve efficiency and aging performance, it can inherently introduce challenges of state of charge (SOC) imbalance within the system. This imbalance, coupled with temperature inhomogeneities in the battery packs, significantly affect the aging rate and further exacerbate system imbalances. To mitigate imbalances, a model predictive control (MPC)-based optimizer for SOC balancing is developed and evaluated against conventional and literature-derived rule-based control (RBC) strategies. Mixed-integer linear programming (MILP) is incorporated into the MPC optimizer to account for non-linear inverter losses during operation. A 1D thermal simulation, developed in this study, is used to analyze the temperature imbalances caused by these control strategies. The simulation estimates the spatial temperature distribution within each pack at the end of the operation, considering internal dissipative losses in the battery modules under fixed boundary conditions for passive air cooling. The comparative case study conducted in this work focuses on key performance metrics such as availability index (AI), fulfilment factor (FF), inverter and battery efficiencies, and state of health (SOH). These metrics are computed by coupling the power split control strategies with 1D thermal and aging estimation models through an equivalent circuit model (ECM). It suggests that due to the delayed balance of the SOC and non-uniform power distribution in RBC strategies, the availability and energy throughput of the system is lower than the desired 100% achieved using MPC. In addition, higher battery pack temperatures of up to 314 K in one of the RBC strategies were estimated, while MPC control induced a maximum temperature of up to 300 K thereby also achieving more balanced temperatures across packs. With the help of the SOC and temperature profiles during their operation, these control strategies are compared for their aging. MPC control strategy exhibited the lowest drop in state of health due to maintaining lower temperatures and mean SOC levels.